The Interplay Between The Interplay Between Research Innovation and Research Innovation and

Federal Statistical PracticeFederal Statistical Practice

Stephen E. Fienberg

Department of Statistics

Center for Automated Learning & Discovery

Carnegie Mellon University

Pittsburgh PA

Some ThemesSome Themes

• Methodological innovation comes from many places and in different colors and flavors.

• Importance of cross-fertilization.

• Cycle of innovation.

• Examples: Bayesian inference, Log-linear models, Missing data and imputation, X-11-ARIMA.

Some Themes (cont.)Some Themes (cont.)

• Statistical thinking for non-statistical problems:– e.g., disclosure limitation.

• Putting several innovations to work simultaneously:– New proposal for census adjustment.

• New challenges

Methodological Innovation in Methodological Innovation in Statistics Statistics

• Comes from many places and in different colors and flavors:– universities:

• statisticians.

• other methodologists.

– government agencies.– Private industry.– nonprofits, e.g., NISS.– committees at the NRC.

Role of Statistical ModelsRole of Statistical Models

• “All models are wrong, but some models are useful.” John Tukey?

• Censuses and surveys attempt to describe and measure stochastic phenomena:– 1977 conference story.– U.S. census coverage assessment:

• “Enumeration”.

• Accuracy and Coverage Evaluation (ACE) survey.

• Demographic Analysis.

Importance of Cross-Importance of Cross-FertilizationFertilization

• Between government and academia.• Among fields of application:

– e.g., agriculture, psychology, computer science

• Between methodological domains e.g., sample surveys and experimental design: Jan van den Brakel Ph.D. thesis, EUR

• Using other fields to change statistics e.g., cognitive aspects of survey design:Krosnick and Silver; Conrad and Shober

Cycle of InnovationCycle of Innovation

• Problem need

• Formal formulation and abstraction– implementation on original problem

• Generalizations across domains

• General statistical theory

• Reapplication to problem and development of extensions– reformulation

Example 1: Bayesian InferenceExample 1: Bayesian Inference

• Laplace– role of inverse probability.– ratio-estimation for population estimation.

• Empirical Bayes and shrinkage (borrowing strength) - hierarchical models.

• NBC election night prediction model.• Small area estimation.

Elliott and Little on census adjustment

Singh, Folsom, and Vaish

Example 2: Log-linear ModelsExample 2: Log-linear Models

• Deming-Stephan iterative proportional fitting algorithm (raking).

• Log-linear models and MLEs:– margins are minimal sufficient statistics.– implications for statistical reporting.

• Some generalizations: generalized IPF, graphical models, exponential families.

• Model-based inference for raking.

Graphical & Decomposable Graphical & Decomposable Log-linear ModelsLog-linear Models

• Graphical models defined in terms of simultaneous conditional independence relationships or absence of edges in graph.

Example:

• Decomposable models correspond to triangulated graphs.

7

2 3

41

2 5

6

Example 3: Missing Data and Example 3: Missing Data and ImputationImputation

• Missing data problems in survey and censuses.– solutions: cold deck and hot deck imputation

• Rubin 1974 framework representing missingness as random variable.

• 1983 CNSTAT Report, Madow et al (3 vol.).• Rubin (1997) - Bayesian approach of multiple

imputation.– NCHS and other agency implementations session on imputation and missing data

Example 4: X-11-ARIMAExample 4: X-11-ARIMA

• BLS seasonal adjustment methods:– X-11 and seasonal factor method (Shishkin et al., 1967)

• ARIMA methods a la Box-Jenkins (1970):– Cleveland and Tiao (1976).– X-11 + ARIMA =X-11/ARIMA (Dagum, 1978).

• Levitan Commission Report (1979).

• X-12-ARIMA.Burck and Salama

Statistical Thinking for Non-Statistical Thinking for Non-Statistical Problems Statistical Problems

• Disclosure limitation was long thought of as non-statistical problem.

• Duncan and Lambert (1986, 1989) and others explained statistical basis.

• New methods for bounds for table entries as well as new perturbation methods are intimately linked to log-linear models.

NISS Disclosure Limitation Project - Karr and Sanil

Query System Illustration Query System Illustration ((kk=3)=3)

Challenge: Scaling up approach for large k.

Bounds for Entries in Bounds for Entries in kk-Way -Way Contingency TableContingency Table

• Explicit formulas for sharp bounds if margins correspond to cliques in decomposable graph. (Dobra and Fienberg , 2000)– Upper bound: minimum of relevant margins.– Lower bound: maximum of zero, or sum of relevant

margins minus separators.• Example:

– cliques are {14}, {234}, {345}, {456}, {567}– separators are {4}, {34},

{45}, {56}7

2 3

41

2 5

6

More Bound ResultsMore Bound Results

• Log-linear model related extensions for– reducible graphical case. – if all (k-1) dimensional margins fixed.

• General “tree-structured” algorithm. Dobra (2000)

– Applied to 16-way table in a recent test.

• Relationship between bounds results and methods for perturbing tables.

• Measures of risk and their role.

NISS Table Server: 8-Way TableNISS Table Server: 8-Way Table

Census EstimationCensus Estimation

• 2000 census adjustment model uses variant of dual systems estimation, combining census and ACE data, to correct for – omissions.– erroneous enumerations (subtracted out before DSE

is applied).

• DSE is based on log-linear model of independence.UK and US papers on DSE adjustment methods

Sample

In Out Total

In a b n1

Out c d?? N -n1

Total n2 N - n2 N??N = n1 n2/a^

Census

Dual Systems SetupDual Systems Setup

Putting Several Innovations to Putting Several Innovations to Work SimultaneouslyWork Simultaneously

• Third system for each block based on administrative records - StARS/AREX

• Log-linear models allow us to model dependence between census and ACE:– in all K blocks have census and AREX data.– in sample of k blocks also have ACE data.– missing data on ACE in remaining K-k blocks.

Administrative List P A

Sample Sample P A P A

P 58 12 69 41 n = 268 A 11 43 34 -

Census

Triple System ApproachTriple System Approach

• Example of small minority stratum from 1988 St. Louis census dress rehearsal.

New Bayesian ModelNew Bayesian Model

• Bayesian triple-systems model:– correction for EEs in census and administrative

records.– missing ACE data in K-k blocks.– dependencies (heterogeneity) among lists.– smoothing across blocks and/or strata using

something like logistic regression model.

• Revised block estimates to borrow strength across blocks and from new source.

New ChallengesNew Challenges

Challenges of Challenges of Multiple-Media Survey Data Multiple-Media Survey Data

• Example: Wright-Patterson A.F. Base Sample Survey– Demographic data PLUS three 3-dimensional

full-body laser surface scans per respondent.– Interest in “functionals” measured from scans.

• Ultimately will have 50 MB of data for each of 10,000 individuals in U.S. and The Netherlands/Italy.

Some Methodological Issues Some Methodological Issues With Image DataWith Image Data

• Data storage and retrieval.

• Data reduction, coding, and functionals:– design vs. model-based inference.

• Disclosure limitation methodology.

Standing Statistics On Its HeadStanding Statistics On Its Head